o
    hU                     @   sz  d dl mZ d dlmZ d dlmZ d dlmZ d dlm	Z	 d dl
mZ d dlmZmZ d dlmZmZmZmZmZmZmZmZmZ d d	lmZmZmZmZmZmZm Z  d d
l!m"Z" G dd deZ#dd Z$G dd dZ%G dd dZ&G dd dZ'e%e'e'e&dZ(G dd de eZ)G dd de)Z*dd Z+G dd de)Z,dd Z-G d d! d!e)Z.d"d# Z/G d$d% d%e)Z0d&d' Z1d(S ))    )prod)Basic)pi)S)exp)
multigamma)sympify_sympify)	ImmutableMatrixInverseTraceDeterminantMatrixSymbol
MatrixBase	Transpose	MatrixSetmatrix2numpy)_value_checkRandomMatrixSymbolNamedArgsMixinPSpace_symbol_converterMatrixDomainDistribution)import_modulec                   @   sf   e Zd ZdZdd Zedd Zedd Zedd Zed	d
 Z	edd Z
dd ZdddZdS )MatrixPSpacezD
    Represents probability space for
    Matrix Distributions.
    c                 C   s@   t |}t|t|}}|jr|jstdt| ||||S )NzDimensions should be integers)r   r	   
is_integer
ValueErrorr   __new__)clsZsymdistributionZdim_nZdim_m r!   f/home/www/facesmatcher.com/frenv_anti/lib/python3.10/site-packages/sympy/stats/matrix_distributions.pyr      s
   zMatrixPSpace.__new__c                 C   
   | j d S )N   argsselfr!   r!   r"   <lambda>       
 zMatrixPSpace.<lambda>c                 C   r#   Nr   r%   r'   r!   r!   r"   r)   !   r*   c                 C   s   t | j| jjS N)r   symbolr    setr'   r!   r!   r"   domain#   s   zMatrixPSpace.domainc                 C   s   t | j| jd | jd | S )N      )r   r-   r&   r'   r!   r!   r"   value'   s   zMatrixPSpace.valuec                 C   s   | j hS r,   )r2   r'   r!   r!   r"   values+      zMatrixPSpace.valuesc                 G   s4   | t}t|dkst|tstd| j|S )Nr$   ztCurrently, no algorithm has been implemented to handle general expressions containing multiple matrix distributions.)Zatomsr   len
isinstanceNotImplementedErrorr    pdf)r(   exprr&   Zrmsr!   r!   r"   compute_density/   s   
zMatrixPSpace.compute_densityr!   scipyNc                 C   s   | j | jj|||diS )zu
        Internal sample method

        Returns dictionary mapping RandomMatrixSymbol to realization value.
        )libraryseed)r2   r    sample)r(   sizer<   r=   r!   r!   r"   r>   7   s   zMatrixPSpace.sampler!   r;   N)__name__
__module____qualname____doc__r   propertyr    r-   r/   r2   r3   r:   r>   r!   r!   r!   r"   r      s    


r   c                 C   sB   t tt|}|| }|j|  |j}t| ||d |d }|jS )Nr   r$   )listmapr   check	dimensionr   r2   )r-   r   r&   distdimZpspacer!   r!   r"   rv@   s   
rL   c                   @   &   e Zd ZdZdddZedd ZdS )SampleMatrixScipyz7Returns the sample from scipy of the given distributionNc                 C      |  |||S r,   )_sample_scipyr   rJ   r?   r=   r!   r!   r"   r   K      zSampleMatrixScipy.__new__c           
         s   ddl m  ddl} fdd fddd}dd d	d d}| }|jj|vr,dS |du s5t|tr=|jj	|d
}n|}||jj |t
||}	|	|||jj | S )zSample from SciPy.r   )statsNc                    s     j jt| jt| jt|dS )N)Zdfscaler?   )Zwishartrvsintnr   scale_matrixfloatrJ   r?   
rand_stateZscipy_statsr!   r"   r)   U   s    z1SampleMatrixScipy._sample_scipy.<locals>.<lambda>c                    s.    j jt| jtt| jtt| jt||dS )N)meanrowcovcolcovr?   Zrandom_state)Zmatrix_normalrU   r   location_matrixrY   scale_matrix_1scale_matrix_2rZ   r\   r!   r"   r)   W   s
    

WishartDistributionMatrixNormalDistributionc                 S      | j jS r,   rX   shaperJ   r!   r!   r"   r)   ^       c                 S   rf   r,   r`   rh   ri   r!   r!   r"   r)   _   rj   r=   )r;   rS   numpykeys	__class__rA   r6   rV   randomdefault_rngr   reshape)
r   rJ   r?   r=   rm   Zscipy_rv_mapsample_shape	dist_listr[   sampr!   r\   r"   rP   N   s    


zSampleMatrixScipy._sample_scipyr,   )rA   rB   rC   rD   r   classmethodrP   r!   r!   r!   r"   rN   I   s
    
rN   c                   @   rM   )SampleMatrixNumpyz7Returns the sample from numpy of the given distributionNc                 C   rO   r,   )_sample_numpyrQ   r!   r!   r"   r   s   rR   zSampleMatrixNumpy.__new__c           
      C   s   i }i }|  }|jj|vrdS ddl}|du st|tr%|jj|d}n|}||jj |t||}	|		|||jj | S )zSample from NumPy.Nr   rl   )
rn   ro   rA   rm   r6   rV   rp   rq   r   rr   )
r   rJ   r?   r=   Znumpy_rv_maprs   rt   rm   r[   ru   r!   r!   r"   rx   v   s   zSampleMatrixNumpy._sample_numpyr,   )rA   rB   rC   rD   r   rv   rx   r!   r!   r!   r"   rw   o   s
    
rw   c                   @   rM   )SampleMatrixPymcz6Returns the sample from pymc of the given distributionNc                 C   rO   r,   )_sample_pymcrQ   r!   r!   r"   r      rR   zSampleMatrixPymc.__new__c           	   	      s   zddl  W n ty   ddl Y nw  fdd fddd}dd dd d	}| }|jj|vr6dS ddl}|d
|j	  
  ||jj |  jt|dd|dddd }W d   n1 siw   Y  ||||jj | S )zSample from PyMC.r   Nc                    s0    j dt| jtt| jtt| jt| jjdS )NX)mur^   r_   rh   )MatrixNormalr   r`   rY   ra   rb   rh   ri   pymcr!   r"   r)      s    


z/SampleMatrixPymc._sample_pymc.<locals>.<lambda>c                    s    j dt| jt| jtdS )Nr{   )nur   )ZWishartBartlettrV   rW   r   rX   rY   ri   r~   r!   r"   r)      s    )re   rd   c                 S   rf   r,   rg   ri   r!   r!   r"   r)      rj   c                 S   rf   r,   rk   ri   r!   r!   r"   r)      rj   rc   r   r$   F)ZdrawschainsZprogressbarZrandom_seedZreturn_inferencedataZcompute_convergence_checksr{   )r   ImportErrorpymc3rn   ro   rA   logging	getLoggersetLevelERRORZModelr>   r   rr   )	r   rJ   r?   r=   Zpymc_rv_maprs   rt   r   sampsr!   r~   r"   rz      s*   


 zSampleMatrixPymc._sample_pymcr,   )rA   rB   rC   rD   r   rv   rz   r!   r!   r!   r"   ry      s
    
ry   )r;   r   r   rm   c                   @   s6   e Zd ZdZdd Zedd Zdd ZdddZd
S )MatrixDistributionz1
    Abstract class for Matrix Distribution.
    c                 G   s    dd |D }t j| g|R  S )Nc                 S   s&   g | ]}t |trt|nt|qS r!   )r6   rF   r
   r	   ).0argr!   r!   r"   
<listcomp>   s
    z.MatrixDistribution.__new__.<locals>.<listcomp>)r   r   )r   r&   r!   r!   r"   r      s   zMatrixDistribution.__new__c                  G   s   d S r,   r!   r%   r!   r!   r"   rH      s   zMatrixDistribution.checkc                 C   s   t |tr	t|}| |S r,   )r6   rF   r
   r8   )r(   r9   r!   r!   r"   __call__   s   

zMatrixDistribution.__call__r!   r;   Nc                 C   sd   g d}||vrt dt| t|std| t| | ||}|dur(|S t d| jj|f )zo
        Internal sample method

        Returns dictionary mapping RandomSymbol to realization value.
        )r;   rm   r   r   z&Sampling from %s is not supported yet.zFailed to import %sNz4Sampling for %s is not currently implemented from %s)r7   strr   r   _get_sample_class_matrixrvro   rA   )r(   r?   r<   r=   Z	librariesr   r!   r!   r"   r>      s   
zMatrixDistribution.sampler@   )	rA   rB   rC   rD   r   staticmethodrH   r   r>   r!   r!   r!   r"   r      s    
r   c                   @   <   e Zd ZdZedd Zedd Zedd Zdd	 Z	d
S )MatrixGammaDistributionalphabetarX   c                 C   s>   t |tst|jd t|jd t| jd t|jd d S )N+The shape matrix must be positive definite.Should be square matrix#Shape parameter should be positive.z#Scale parameter should be positive.r6   r   r   is_positive_definite	is_squareis_positiver   r!   r!   r"   rH      s
   
zMatrixGammaDistribution.checkc                 C      | j jd }t||tjS r+   rX   rh   r   r   Realsr(   kr!   r!   r"   r.         zMatrixGammaDistribution.setc                 C   rf   r,   rg   r'   r!   r!   r"   rI     r4   z!MatrixGammaDistribution.dimensionc           
      C   s   | j | j| j}}}|jd }t|trt|}t|ttfs(t	dt
| t| | | }tt||||  t||  }t||  }t||t|d d   }	|| |	 S )Nr   4%s should be an isinstance of Matrix or MatrixSymbolr$   r0   )r   r   rX   rh   r6   rF   r
   r   r   r   r   r   r   r   r   r   r   )
r(   xr   r   rX   psigma_inv_xterm1term2term3r!   r!   r"   r8     s   

"zMatrixGammaDistribution.pdfN
rA   rB   rC   Z	_argnamesr   rH   rE   r.   rI   r8   r!   r!   r!   r"   r      s    
	

r   c                 C   s$   t |tr	t|}t| t|||fS )a  
    Creates a random variable with Matrix Gamma Distribution.

    The density of the said distribution can be found at [1].

    Parameters
    ==========

    alpha: Positive Real number
        Shape Parameter
    beta: Positive Real number
        Scale Parameter
    scale_matrix: Positive definite real square matrix
        Scale Matrix

    Returns
    =======

    RandomSymbol

    Examples
    ========

    >>> from sympy.stats import density, MatrixGamma
    >>> from sympy import MatrixSymbol, symbols
    >>> a, b = symbols('a b', positive=True)
    >>> M = MatrixGamma('M', a, b, [[2, 1], [1, 2]])
    >>> X = MatrixSymbol('X', 2, 2)
    >>> density(M)(X).doit()
    exp(Trace(Matrix([
    [-2/3,  1/3],
    [ 1/3, -2/3]])*X)/b)*Determinant(X)**(a - 3/2)/(3**a*sqrt(pi)*b**(2*a)*gamma(a)*gamma(a - 1/2))
    >>> density(M)([[1, 0], [0, 1]]).doit()
    exp(-4/(3*b))/(3**a*sqrt(pi)*b**(2*a)*gamma(a)*gamma(a - 1/2))


    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Matrix_gamma_distribution

    )r6   rF   r
   rL   r   )r-   r   r   rX   r!   r!   r"   MatrixGamma  s   
+r   c                   @   r   )rd   rW   rX   c                 C   s2   t |tst|jd t|jd t| jd d S )Nr   r   r   r   r   r!   r!   r"   rH   L  s   
zWishartDistribution.checkc                 C   r   r+   r   r   r!   r!   r"   r.   U  r   zWishartDistribution.setc                 C   rf   r,   rg   r'   r!   r!   r"   rI   Z  r4   zWishartDistribution.dimensionc           	      C   s   | j | j}}|jd }t|trt|}t|ttfs$tdt	| t
| | td }tt|d|| td  t|td |  }t|| td  }t|t|| d d  }|| | S )Nr   r   r0   r$   )rW   rX   rh   r6   rF   r
   r   r   r   r   r   r   r   r   r   r   )	r(   r   rW   rX   r   r   r   r   r   r!   r!   r"   r8   ^  s   

2zWishartDistribution.pdfNr   r!   r!   r!   r"   rd   H  s    

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rd   c                 C   s"   t |tr	t|}t| t||fS )a  
    Creates a random variable with Wishart Distribution.

    The density of the said distribution can be found at [1].

    Parameters
    ==========

    n: Positive Real number
        Represents degrees of freedom
    scale_matrix: Positive definite real square matrix
        Scale Matrix

    Returns
    =======

    RandomSymbol

    Examples
    ========

    >>> from sympy.stats import density, Wishart
    >>> from sympy import MatrixSymbol, symbols
    >>> n = symbols('n', positive=True)
    >>> W = Wishart('W', n, [[2, 1], [1, 2]])
    >>> X = MatrixSymbol('X', 2, 2)
    >>> density(W)(X).doit()
    exp(Trace(Matrix([
    [-1/3,  1/6],
    [ 1/6, -1/3]])*X))*Determinant(X)**(n/2 - 3/2)/(2**n*3**(n/2)*sqrt(pi)*gamma(n/2)*gamma(n/2 - 1/2))
    >>> density(W)([[1, 0], [0, 1]]).doit()
    exp(-2/3)/(2**n*3**(n/2)*sqrt(pi)*gamma(n/2)*gamma(n/2 - 1/2))

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Wishart_distribution

    )r6   rF   r
   rL   rd   )r-   rW   rX   r!   r!   r"   Wishartl  s   
(r   c                   @   r   )re   )r`   ra   rb   c                 C   s   t |tst|jd t |tst|jd t|jd t|jd | jd }| jd }t|jd |kdt|t|f  t|jd |kdt|t|f  d S )Nr   )Scale matrix 1 should be be square matrix)Scale matrix 2 should be be square matrixr   r$   )Scale matrix 1 should be of shape %s x %s)Scale matrix 2 should be of shape %s x %s)r6   r   r   r   r   rh   r   )r`   ra   rb   rW   r   r!   r!   r"   rH     s   


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zMatrixNormalDistribution.checkc                 C      | j j\}}t||tjS r,   r`   rh   r   r   r   r(   rW   r   r!   r!   r"   r.     r   zMatrixNormalDistribution.setc                 C   rf   r,   rk   r'   r!   r!   r"   rI     r4   z"MatrixNormalDistribution.dimensionc           
      C   s   | j | j| j}}}|j\}}t|trt|}t|ttfs(t	dt
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   r   r   r   r   r   r   r   r   r   r   r   )
r(   r   MUVrW   r   r   numZdenr!   r!   r"   r8     s   

$@zMatrixNormalDistribution.pdfNr   r!   r!   r!   r"   re     s    

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re   c                 C   sL   t |tr	t|}t |trt|}t |trt|}|||f}t| t|S )a  
    Creates a random variable with Matrix Normal Distribution.

    The density of the said distribution can be found at [1].

    Parameters
    ==========

    location_matrix: Real ``n x p`` matrix
        Represents degrees of freedom
    scale_matrix_1: Positive definite matrix
        Scale Matrix of shape ``n x n``
    scale_matrix_2: Positive definite matrix
        Scale Matrix of shape ``p x p``

    Returns
    =======

    RandomSymbol

    Examples
    ========

    >>> from sympy import MatrixSymbol
    >>> from sympy.stats import density, MatrixNormal
    >>> M = MatrixNormal('M', [[1, 2]], [1], [[1, 0], [0, 1]])
    >>> X = MatrixSymbol('X', 1, 2)
    >>> density(M)(X).doit()
    exp(-Trace((Matrix([
    [-1],
    [-2]]) + X.T)*(Matrix([[-1, -2]]) + X))/2)/(2*pi)
    >>> density(M)([[3, 4]]).doit()
    exp(-4)/(2*pi)

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Matrix_normal_distribution

    )r6   rF   r
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)
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r}   c                   @   r   )MatrixStudentTDistribution)r   r`   ra   rb   c                 C   s   t |tst|jdkd t |tst|jdkd t|jdkd t|jdkd |jd }|jd }t|jd |kdt|t|f  t|jd |kdt|t|f  t| jdkd	 d S )
NFr   r   r   r   r$   r   r   z#Degrees of freedom must be positive)r6   r   r   r   r   rh   r   r   )r   r`   ra   rb   rW   r   r!   r!   r"   rH     s   


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z MatrixStudentTDistribution.checkc                 C   r   r,   r   r   r!   r!   r"   r.     r   zMatrixStudentTDistribution.setc                 C   rf   r,   rk   r'   r!   r!   r"   rI     r4   z$MatrixStudentTDistribution.dimensionc           
      C   s  ddl m} t|trt|}t|ttfstdt| | j	| j
| j| jf\}}}}|j\}}t|| | d d |t|| d   t|| d   t|| d  t|| d d |  }	|	t||t|||  t| t||   || | d  d   S )Nr   )eyer   r$   r0   )Zsympy.matrices.denser   r6   rF   r
   r   r   r   r   r   r`   ra   rb   rh   r   r   r   r   r   )
r(   r   r   r   r   OmegaSigmarW   r   Kr!   r!   r"   r8     s   

<$0zMatrixStudentTDistribution.pdfNr   r!   r!   r!   r"   r     s    

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r   c                 C   sN   t |tr	t|}t |trt|}t |trt|}||||f}t| t|S )a  
    Creates a random variable with Matrix Gamma Distribution.

    The density of the said distribution can be found at [1].

    Parameters
    ==========

    nu: Positive Real number
        degrees of freedom
    location_matrix: Positive definite real square matrix
        Location Matrix of shape ``n x p``
    scale_matrix_1: Positive definite real square matrix
        Scale Matrix of shape ``p x p``
    scale_matrix_2: Positive definite real square matrix
        Scale Matrix of shape ``n x n``

    Returns
    =======

    RandomSymbol

    Examples
    ========

    >>> from sympy import MatrixSymbol,symbols
    >>> from sympy.stats import density, MatrixStudentT
    >>> v = symbols('v',positive=True)
    >>> M = MatrixStudentT('M', v, [[1, 2]], [[1, 0], [0, 1]], [1])
    >>> X = MatrixSymbol('X', 1, 2)
    >>> density(M)(X)
    gamma(v/2 + 1)*Determinant((Matrix([[-1, -2]]) + X)*(Matrix([
    [-1],
    [-2]]) + X.T) + Matrix([[1]]))**(-v/2 - 1)/(pi**1.0*gamma(v/2)*Determinant(Matrix([[1]]))**1.0*Determinant(Matrix([
    [1, 0],
    [0, 1]]))**0.5)

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Matrix_t-distribution

    )r6   rF   r
   rL   r   )r-   r   r`   ra   rb   r&   r!   r!   r"   MatrixStudentT/  s   
,
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r   N)2mathr   Zsympy.core.basicr   Zsympy.core.numbersr   Zsympy.core.singletonr   Z&sympy.functions.elementary.exponentialr   Z'sympy.functions.special.gamma_functionsr   Zsympy.core.sympifyr   r	   Zsympy.matricesr
   r   r   r   r   r   r   r   r   Zsympy.stats.rvr   r   r   r   r   r   r   Zsympy.externalr   r   rL   rN   rw   ry   r   r   r   r   rd   r   re   r}   r   r   r!   r!   r!   r"   <module>   s:    ,$,	&)0%2$/-52